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Shock and Vibration
Volume 14, Issue 3, Pages 169-179

Effect of Tapering on Natural Frequencies of Rotating Beams

A. Bazoune

Department of Mechanical Engineering, King Fahd University of Petroleum & Minerals, KFUPM BOX 579, Dhahran 31261, KSA

Received 13 April 2006; Accepted 13 May 2006

Copyright © 2007 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The problem of free vibration of a rotating tapered beam is investigated by developing explicit expressions for the mass, elastic and centrifugal stiffness matrices in terms of the taper ratios. This investigation takes into account the effect of tapering in two planes, the effect of hub radius as well as the stiffening effect of rotation. The equations of motion are derived; the associated generalized eigenvalue problem is defined in conjunction with a suitable Lagrangian form and solved for a wide range of parameter changes. The effect of tapering on the natural frequencies of the beam is examined with all parameter changes present. Results are compared with those available in literature and are found to be in excellent agreement.